Answer

54h(2g-1)(g-1)

Work Step by Step

Given the polynomial
$108hg^{2}$ - 162hg + 54h
We see that the three terms have a common factor of 54h so we factor out a 54h.
54h($2g^{2}$ - 3g + 1)
*** We break of the middle term into two factors that add to give -3 and multiply to give +2. The two numbers are -2 and -1.
54h($2g^{2}$ - 2g - 1g + 1)
We take the GCD of the first two and the GCD of the last two terms.
54h(2g(g-1)-1(g-1))
We take (g-1) and factor it out which gives us.
54h(2g-1)(g-1)